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The high-mass X-ray binary Vela X-1 exhibits large, rapid variations in the periodicity of its X-ray pulses. Given that the pulsing of X-rays is attributed to the rotation of a neutron star, these variations imply rapid changes in the rotation rate of the accreting neutron star. The source of angular momentum driving these variations in the rotation rate is assumed to be the accreting material that fuels the X-ray emission. Over the past several years two-dimensional hydrodynamic simulations of accretion onto a compact object have shown the presence of an instability in which the accretion bowshock swings violently from one side to the other. This ``flip-flop'' of the bowshock/accretion flow leads to rapid changes in the sign of the accreted angular momentum as well as a large magnitude of accreted angular momentum despite a lack of strong asymmetry in the incoming flow. While these results look very suggestive of the spin behavior of wind-fed X-ray pulsars, the presence of the flip-flop instability in three dimensions has yet to be shown. We present 3D hydrodynamic simulations of the wind accretion in high-mass X-ray binaries, showing the presence of the flip-flop in 3D much as it appears in 2D simulations.
